Brees and the Saints went from leading by 17 to trailing midway through the fourth quarter. The Cowboys were about to seal the victory with a long pass play when safety Malcolm Jenkins swiped the ball back and Brees drove 89 yards for a go-ahead touchdown 1:55 left. Dallas’ David Buehler narrowly missed a 59-yard field goal with 25 seconds left that would’ve tied it, and the Saints held on for a 30-27 victory Thursday.

“It was kind of a gut-check win,” New Orleans coach Sean Payton said.

Payton appeared to be trying to call timeout as the ball was snapped for Buehler’s kick, which would’ve given the Cowboys another chance. But the officials didn’t give it to him, so the play stood.

“Fortunately, I did not,” Payton said.

The Saints, playing on the holiday for the first time, won their fourth straight and fifth in six games to improve to 8-3. Dallas (3-8) lost for the first time in three games since Garrett became interim coach.

“I think we demonstrated again what we’ve done the last few weeks — battle and fight,” Garrett said. “There were a lot of things to be proud of. Guys played with a lot of passion, energy and enthusiasm. … But you’ve got to get the bottom line right. We didn’t get it done.”

Sixteen years ago, Garrett was a third-string quarterback making a rare start in place of Troy Aikman when the Cowboys fell behind Brett Favre and the Packers 17-3. Garrett rallied them a 42-31 victory that’s among the most stirring in team lore.

This one would’ve been up there, too. Instead, it may go down with Leon Lett’s snowy gaffe in 1993 as one that got away.

“This is a game that, if you let it, it will rip your heart out,” Dallas quarterback Jon Kitna said. “You feel like you played well enough to win — you just didn’t.”

The Cowboys trailed 17-0 after the first three times the Saints had the ball. New Orleans also were up 20-3 just before halftime.

Garrett constantly preaches to his club that they’re going to face adversity, so he wants them to be ready to handle it. The same group that fell apart under his predecessor, Wade Phillips, showed lots of spunk with their response to this challenge.

Buehler made a career-best 53-yarder as the second quarter ended to start a run of points on four straight possession. After a punt ended the streak, Dallas bounced back on the next series, getting a 1-yard touchdown run from Tashard Choice to go ahead 27-23 with 5:51 left.

The Cowboys were on their way to stretching the lead or killing the clock when Roy Williams broke free with a catch and raced 47 yards toward the end zone, following a block by Miles Austin. He switched the ball from one hand to another to avoid a defender he saw. But he didn’t see Jenkins and got the ball plucked from him at the 11.

“I lost the ball game,” Williams said. “I let my teammates down. I need to fall down. We run the clock down and win the game. I was trying to make a play and they did a good job. It’s late in the game. That’s the nail in the coffin. We had the momentum going our way. We were there. That was a W. I get tackled, we get in the end zone and we win. I fall down and we win.”

Jenkins said he chased the play with only one thought — “get the ball out.”

“He didn’t see me from the blind side,” Jenkins said. “A bad play turned good for us. Not only ripped it out, it just kind of fell in my stomach.”

Brees then drove the Saints 89 yards in five plays. He hit Robert Meachem for 55 yards and Lance Moore on a 12-yard touchdown strike.

The Cowboys had one try left, and Kitna got them close enough to give Buehler’s powerful leg a try. The kick had plenty of distance, but fluttered left before reaching the uprights.

The game was filled with would-be heroes like Miles Austin, who kick-started Dallas’ rally by taking an end around 60 yards for a touchdown on the second play of the second half, and would-be goats like Reggie Bush, who had a forgettable return from an eight-game layoff because of a broken foot. He dropped a likely touchdown pass with the Saints up 20-13, then fumbled on a punt return to set up the Cowboys’ touchdown that made it 23-20.

Brees finished 23 of 39 for 352 yards with a touchdown and an interception. That was another play that would’ve been a bigger deal had the outcome been reversed — it bounced off the hands of tight end Jimmy Graham and into the hands of Dallas safety Gerald Sensabaugh, leading to Choice’s go-ahead score.

The Saints opened the game so crisply, they looked capable of returning to Cowboys Stadium for the Super Bowl. Brees marched them 80 yards in four plays on the opening drive, never even seeing a second down. They intercepted a screen pass and Garrett Hartley kicked a career-best 50-yard field goal, then Brees drove for another touchdown and the 17-0 lead.

Marques Colston finished with six catches for 105 yards for New Orleans, and Devery Henderson had 97 yards receiving. Kitna was 30 of 42 for 313 yards, and Jason Witten had 10 catches for 99 yards.